Archive for the Science Category

Vector movement game units

Posted in Intercept, Other vector movemet systems, Rules, Science, Traveller, Vector movement on July 16, 2019 by Anders Backman

When you create your own vector movement system, as I am sure everyone does, you need to determine what map scale, turn length and acceleration units are. There is an obvious formula from school that most seem to use and but will argue for why this is wrong and why one should instead use another formula, also from school.

Plotting example


Typically one decide on the map scale first (how large will the hexes, squares, inches or centimeters be?). Deciding on scale is mainly about what you want in your maps, do you want planets to be one unit or less in scale? Do want to show Earth and the moon on the same map? Do you want to fit the inner solar system on your map, like Triplanetary? And so on.

Some examples:

  • Intercept 10 000 km per square, 15 minute turns, 1G per square.
  • Intercept large scale 100 000 km per square, 60 minute turns, 1G per square.
  • Traveller LBB 1000 km per inch, 5 minute turns, 1G per inch.
  • Mayday by GDW 300 000 km per hex, 100 minute turns, 1G per hex.
  • Triplanetary ~10 million km per hex, 1 day per turn, ? G per hex.

Intercept let you play using two different scales and switch back and forth as you like, there’s even a smaller scale in the works if I can iron out the problems with planets taking up large parts of the map, that scale will be 1 000 km, 4 minute turns and 1G per square as usual.

We will later calculate what acceleration Triplanetary is likely using based on the distance and time scales and formulas learned.


High school math teaches us two formulas for determining distance traveled, one for when applying constant acceleration from a standstill and another when having constant speed.

The two formulas are:

Formula one and two

Notice how formula 2b is the same as formula 1 but without the 1/2 multiplier. Distances traveled become twice as far in formula 2 so one of them must be wrong, right?

Not so fast! The formula from high school actually looks like this:

Formuila one with prior speed

Formula (3) also take the velocity from the previous turn into account (the v0 term). As v equals a multiplied by t we get our beloved formula (2b) as the first term, or something similar at least.Why is the first term twice as big as the second term? Well, the the first term assumes the speed is constant through the time segment t while the second term treat is as increasing, the distance traveled can be seen as areas in graphs with speed plotted versus time, like this:

Formula and area

If we use formula (3) to determine total distance traveled while t keeping t as the turn length and v as v (n-1) where n is the number of turns we’ll see that as the number of turns increase the grey area will more and more resemble a rectangle (the triangle of the last turn will contribute less and less of a fraction of distance traveled).

Formula graph

The grey area is the distance traveled. If we call one rectangle as 1.0 and one triangle as 0.5 we get the following distances:

  • Turn 1: 1 triangle plus 0 rectangles = 0.5
  • Turn 2: 2 triangles plus 1 rectangle = 2.0
  • Turn 3: 3 triangles plus 3 rectangles = 4.5
  • Turn 4: 4 triangles plus 6 rectangles = 8.0

and so forth…

You see that as the number of turns increases the number of rectangles increases faster than the number of triangles. So, as the number of turns increase the the number of rectangles will outstrip the number of triangles.

In the vector movement systems of Triplanetary, Mayday, Traveller, Intercept etc we use a vector that both represent velocity and acceleration however. So we either decide that one unit length should be correct for acceleration from a standstill but wrong for drifting or accelerating with a prior velocity (1) or we decide that one unit length should be correct for drifting and approach correct when handling prior velocity (2).

Too much theoretical bullshit you say? OK, let’s do a practical example.

Let’s travel from a standstill to the moon as see which of formula (1) or (2) most closely fit (3). We ignore braking at the moon just go to the moon as fast as possible. The average distance between the earth and the moon is 380 000 km so let’s go with that.

Units for formula (1)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 76 squares.

Traveling 76 squares with 1 unit acceleration will be

1+2+3+4+5+6+7+8+9+10+11+12 = 78 units after 12 turns (12 000 s) = 3 h 20 m
(We overshot the moon by 2 squares but this is the closest we could get)

Units for formula (2)

  • A = 10 m/s^2
  • T = 1000 s
  • S = 5000 km

Distance earth – moon will be 38 squares.

1+2+3+4+5+6+7+8+9+10 = 46 units after 10 turns (10 000 s) = 2 h 45 m
(We overshot the moon by 8 squares but this is the closest we could get)

The correct value using formula (3) and setting v0 to zero is (8 718 s) = 2 h 25 m


Sorry about the long winded explanation but for some reason most vector systems get this wrong. Doesn’t matter when you play of course but say you want to travel from earth to the moon using actual mapboard movement you’d find that the travel time would not match the calculated value.

Apollo 11 50 years anniversary July 16 1969

Yes, 50 years ago today a couple of Americans started their travel from earth to the moon , certainly not under constant 1 G acceleration and they made damned sure their velocity was as close to zero as possible before they hit the moon. Apollo 11 did the trip in about half a week.



Sensor types part 1

Posted in Intercept, Rules, Science on September 20, 2018 by Anders Backman

Planet LOS in Star Wars

Space combat takes place at incredible ranges, tens of thousands of kilometers, and unlike in the movies, you won’t see anything through your window; a nuclear detonation for sure, fission or fusion thrusters as pinpoints of light maybe, the plume of a missile just before it hits you, the blinding flash from a laser hitting your ship, but aside from that nothing…

All ships carry sensors to see things around them and this is especially true of warships. All ships will have optical sensors seeing in visual and infrared wavelengths and most will also have radar. More exotic sensors such as neutrino or gravity sensors may be carried by larger or more specialized vessels.

Visual, infrared and radar sensors are mounted on the surface of the hull and can only be used when unfolded and extended, popped out as it is called in the game. Neutrino and mass sensors sees right through the hull so they can be used whether popped out or not. This make them especially suitable for military purposes as they can be used while still protected by the ships armor.


Visual scans are done with optical telescopes collecting light from visible wavelengths.

Light sources can be light from the sun reflected from the hull. How much depends on the strength of the sunlight, the area of the reflecting hull and how reflective the hull material is.

Light can also be directly emitted by a ships thrust, either the intense light from fission or fusion rocket plumes or the much fainter glow from impulse thrusters or floaters (that magic sci-fi blue glow).

The Inverse square law

The light falls off in strength as it spreads from its source, in both dimensions, if range doubles the intensity goes down as 1/2 times 1/2 or 1/4.


Popular media usually depict space as cold but in reality the problem is the opposite, getting rid of heat is hard part and the only viable long term way of doing it is by radiating it away. Every object radiates heat, how much depends on its temperature.

Ships have optical sensors that can either look in visual wavelengths or in infrared to detect objects as they radiate heat to cool. Ships radiate enormous amounts of heat when using fission or fusion thrusters, less infrared is radiated from the power plant when running, ships also radiate a faint heat from the temperature of the hull itself.

The infrared light falls off the same way as visual light, by the square of the distance. A given ship is typically easier to detect visually than by infrared, at least when the ship is in sunlight or if the ship has a running power plant. If the ship is using fission or fusion thrusters it’s about as easy regardless of using infrared or visual scanning. What to use really depends on what you think you are trying to find, tricky.

Plotting board


Everyone is familiar with radar works; you send out radio bursts that bounce off the target and get detected as it comes back.

One problem with radar is that it falls off much faster than visual or infrared does. Radar, although invented during World War II didn’t detect the planet Venus until 1961 yet it can easily be seen by the naked eye. Doesn’t radar waves fall off by the inverse square as visual and infrared does?

Of course they do. The problem is they fall off by the inverse square both going there and coming back again, 1/r^2 going there x 1/r^2 coming back again or, 1/r^4. If this sound weird and hard to grasp think about the following analogy:

You walk at night in a forest with a flashlight in your hand. The flashlight is a powerful maglite showing you the trees out to about 30 meters.

The flashlights range depends on the power of the flashlight but also the quality and focus of the lights parabolic mirror. The light falls off going out, bounces off trees and falls off coming back again, back to your eyes, your detectors, just like a radar.

Let’s say you decide to try your car lights instead. They must be a hundred times more powerful right? And now you can see trees out to about a hundred meters, three times farther or so. Three to the fourth power (3^4) is about a hundred (81) so that terrible range fall off of radar affects flashlights and headlights the same way.


Two men in a rubber raft inspect the wall of photodetectors
of the partly filled Super-Kamiokande neutrino detector (Ars Technica)


Neutrinos are these strange subatomic ghost particles created in fission and fusion reactions. These particles really fleeting, reacting to next to nothing. Build a wall one lightyear thick and half of them still get through. How can one ever hope to detect them with something smaller than a solar system, smaller than a planet even, small enough to fit on a ship?

What you do is you amass an enormous amount of atoms, in the hope that one neutrino might interact with one of them and then surround the mass with super sensitive detectors hoping to catch that one interaction somehow. The first detectors used thousands of cubic meters of water or chlorine as the mass and after waiting a long time they got the first signal from the sun. Imagine that, it took this enormous tank lined with super sensitive detectors sitting for months to detect a single neutrino coming from this enormous fusion reactor we call the sun.

Neutrino detectors in Intercept appear at TL-11 and assumes that some breakthrough has appeared, some resonance to exploit or some other way to make the neutrino detectors much smaller and much more sensitive, still bulky but practical. Neutrinos created in fission or fusion thrusters and fission or fusion power plants are what these detectors see. As the neutrinos leave their source they spread out, just as the visible photons for the visual scans and the infrared photons for the IR scans so the fall off is the same.

Neutrino sensors can only detect fission and fusion thrusters and fission and fusion power plants. On the other hand when they can see targets on planets or right through planets as if they aren’t there at all. In fact, a ship in the planetary shadow scanning towards the sun will be affected by Sunglare as if the planet wasn’t there at all.

Gravity with Thrust


Detecting a nearby mass seems easy. Just measure its gravitational pull on you. Not so easy. Imagine you were locked inside a small box either being a hundred km above earth and falling towards it (let’s ignore air drag completely) or being a light year away in the depth of space.

How can you detect which is case it is? How can you detect how far away earth is and in what direction? In both cases the box and you would be at rest with each other, either falling freely towards earth or just drifting in interstellar space. You could peek out of the box but that would be cheating. There is one difference that you can actually measure, being near earth means you closest point, say your toe, would be pulled towards earth a tiny amount more than your furthest point, say your nose, the difference between these pulls could be measured as a very weak force and this force would grow weaker the farther away from earth you go, a light year away in deep space and you’d measure nothing at all.

This force is called the tidal force and pulls apart parts of objects in a gravity field. The ocean water closest to the moon gets pulled towards the moon relative the water on the other side causing two bulges that move as the earth rotates. Yes that is why there are two tides each 24 hours.

Tidal force falls off as 1/r^3, double the range and the tidal force is 1/2 x 1/2 x 1/2 or 1/8 the strength. This limits the range of mass sensors but on the other hand they can see right through planets and because of the 1/r^3 falloff can scan towards the sun.

Mass sensors detect the mass of a ship directly but usually they detect the much stronger emissions from the gravitic Impulse or Floaters and also any working floorfields. This means that older low tech ships lacking floorfields and relying on fusion or fission for thrust are actually the hardest to detect.

Well, that is all for now. The next article will deal with the practical use of these sensors in Intercept. How to use them effectively and how to avoid being detected by them. Keep the solar wind to yer backside folks!

Tsiolkovsky’s rocket equation

Posted in Intercept, Science with tags , , on December 28, 2012 by Mr Backman

I was fiddling with a TL-8 fission rocket design for going to the moon and back as cheap as possibly when I noticed something strange; going for more advanced materials would lower the mass of the ship and thus increasing its acceleration but it had no effect on delta-V? The design was for an upcoming article on landings, takeoffs, aerobraking, docking and ramming. It turned out to be just a bug and together with this post you can download the updated design spreadsheets, designs etc at the usual location.

Then I realised that the rules doesn’t dwell much on low tech rocket design, delta-V, mass ratios and such. These are the bread and butter of ‘real’ rocket design, and at the core of this rocket science art is the Tsiolkovsky’s rocket equation. Cool name for a post covering up my spreadsheet blunder and here we are.

Tsiolkovsky, Russian rocket pioneer and visionary did all the theoretical work for rocketry way before anyone really thought of rockets in space. He calculated the velocity needed to go to orbit and that to achieve it one should do it in a multi-stage rocket fueled by liquid Hydrogen and Oxygen, this was in 1903. Even before that, in 1896, he derived his famous rocket equation.

A real rocket accelerates by pushing stuff out the back, the faster it pushes and the heavier the stuff it pushes the higher the acceleration. Now, the tricky part is that as the rocket expends reaction mass it gets lighter which also increases acceleration. A rockets acceleration is at its lowest when it starts and at its highest just before it runs out of reaction mass. All this makes it hard to calculate just how much total velocity change a given rocket will have, twice the fuel will not give you twice the velocity change but more etc. Mr Tsiolkovsky helps us here with this simple formula:

Tsiolovsky rocket equaton

  • dV is the total change in velocity (m/s)
  • Vexh is the exhaust velocity (m/s)
  • M0 is the fully fueled mass of the ship (kg)
  • M1 is the empty mass after all fuel is gone (kg)

ln is the natural logarithm (logaritmus naturale) but you already knew that, right.
A derivation of the rocket equation and more facts about the great Konstantin Tsiolkovsky is available at Wikipedia.

So, whenever you design a ship with a fission or fusion rocket you now know how it gets its endurance value. Pay attention to the mass of components and if you can afford it you should try increasing the Material quality as this will reduce mass and increase acceleration Gs and endurance.

Whenever your friends complain about you fiddling with Intercept just tell them that you’re doing rocket science!

Air-raft to orbiting ship

Posted in Science, Traveller on December 29, 2010 by Mr Backman

Various canon Traveller sources state that Air-rafts can reach orbit and in my Traveller campaign precisely that situation arose during my weekend session with my kids. I assume here that the ship we want to match orbit with is in Low Earth Orbit (LEO). The problem is much simpler if the ship is hovering on its contragrav above the planet but that is not what the canon sources say; ‘orbit’ does not mean outside the atmosphere, it means outside the atmosphere with enough speed for centripetal forces to match gravity.

If you dig into the problem there are lots of complications that crop up:

Problems with the air-raft
An open topped vehicle is hardly built for vacuum as this costs a lot extra, so I guess the instrumentation, upholstery etc will break in vacuum. Another problem is that an air-raft produces something like 0.1 G thrust for propulsion which mean (ballpark calculations here) that to reach say 5 km/s orbital velocity they must accelerate for over an hour (ca 5000 seconds).

Problems with the calculations
To match the orbit of a ship the air-raft driver must eyeball the ship and vector (yes, LEO ships can be seen at dusk or dawn by the human eye) and then match that orbit by hand with the air-raft over a more than an hour long acceleration phase. The air-raft will have no instrumentation for orbit matching and the like, just an accelerometer based (Traveller vehicles does not rely on the crude GPS system we use) absolute positional instrument that also indicate height as well as speed gauges. Calculating the orbital mechanics and driving the air-raft to comply is in my opinion a really hard problem for a spaceship pilot and impossible for mere grav-jockeys. If you think orbit matching is a piece of cake try it yourself with the free PC space simulator Orbiter.

IMTU (In My Traveller Universe)
My TL progression differs from canon and GURPS Traveller and this causes even more problems:
(I don’t add gravtech until TL 10, so I can have cultures with jumpdrives without grav and floorfield, ‘Hard-SF with jump’ if you will)
Jumpdrives TL 9
Floaters TL 10
Floorfield TL 11
Gravthrust TL 12
Floater gravbelts TL 13
Reactionless drives TL 13
Gravbelts TL 14
Tractor beams TL 15
Pressor beams TL 16
Rattlers (high freq tractor weapons) TL 17

Floaters are grav ‘thrusters’ that can only negate gravity, they can never create upwards or lateral thrust, just negate the downward pull of gravity. Floaters and gravthrust have ‘thrust’ proportional to local gravity so a 1G (Thrust = mass) floater will negate gravity on all planets, regardless of gravitation (simplifies designing gravvehícles and ‘explains’ why gravthrust is useless for interplanetary travel). Floaters come at TL 10, are much cheaper and require much less power per ‘thrust’ than regular gravthrust. Regular gravthrusters produce floating at the cost of x1/10 thrust (a 1G gravthrust would use 0.1 G for floating and 0.9 G for propulsion for example).
My air-rafts are so cheap they use floaters powered by a fuelcell for lift and turbojet for thrust (both the fuelcell and turbojet are hydrogen powered and need an atmosphere with oxygen to work).

So IMTU the air-rafts cannot reach orbit at all, they cannot even operate in anything near vacuum, fitted with compressors they can work in Very thin atmospheres, but that’s it.

Edit: I have updated the Intercept design system to reflect the TL progression (and no, there are no tractor, pressor or rattlers yet).